my new iphone 12 mini asks for a password when I turn it on. Now it says it is disabled

The issue seems to be, that you have forgotten your phone password and locked yourself out. If that’s the case then restart won’t help you at all. An easy way would be to factory reset your phone via a computer/Desktop though apple iMac or MacBook is recommend, once you reset your phone you can start from the scratch and get your lost data over the iCloud services.

As the scenario is explained, this would be the best way but if you are experiencing a different issue where you know the correct password but your phone is not giving you an option to enter the password by showing the disabled tag, then just wait for the remaining time the phone asks for and if that also doesn’t work then try to get your phone to recovery mode and restart it or try to get it in the recovery mode, connect a computer and update the iOS version from there which might help.

A summery:

1). Factory reset if you don’t remember the password (https://support.apple.com/en-in/HT204306)

2). Get it into the recovery mode and restart the phone (reboot) without updating your phone (https://support.apple.com/en-in/HT201263)

3). Get your phone updated by connecting it to a device via recovery mode and hit on update

I hope this might help

If you forgot the passcode on your iPhone, or your iPhone is disabled -

https://support.apple.com/en-us/HT204306

Following this process, the only way out. The steps given in this link will help you reset the passcode -> If you forgot the passcode for your iPhone, iPad, or iPod touch, or your ...

If you mean that you saw this the first time you turned it on, your phone wasn’t new. Return it for a refund or exchange.